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Perfect sampling for infinite server and loss systems

Part of: Special processes Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  21 March 2016

Jose Blanchet  and
Jing Dong
Jose Blanchet*
Affiliation:
Columbia University
Jing Dong*
Affiliation:
Columbia University
*
∗ Postal address: Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027, USA. Email address: [email protected]
∗∗ Current address: Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL 60208, USA. Email address: [email protected]
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Abstract

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We present the first class of perfect sampling (also known as exact simulation) algorithms for the steady-state distribution of non-Markovian loss systems. We use a variation of dominated coupling from the past. We first simulate a stationary infinite server system backwards in time and analyze the running time in heavy traffic. In particular, we are able to simulate stationary renewal marked point processes in unbounded regions. We then use the infinite server system as an upper bound process to simulate the loss system. The running time analysis of our perfect sampling algorithm for loss systems is performed in the quality-driven (QD) and the quality-and-efficiency-driven regimes. In both cases, we show that our algorithm achieves subexponential complexity as both the number of servers and the arrival rate increase. Moreover, in the QD regime, our algorithm achieves a nearly optimal rate of complexity.

Keywords

Perfect samplingdominated coupling from the pastinfinite server queueloss queuerenewal point processmany-server asymptotics

MSC classification

Primary: 65C05: Monte Carlo methods 68U20: Simulation
Secondary: 60K25: Queueing theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 47 , Issue 3 , September 2015 , pp. 761 - 786
Copyright
Copyright © Applied Probability Trust 2015 

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